In Eureka, they have destroyed quite a few of the Jeeps that belong to Sheriff Carter, averaging about one Jeep an episode. I was watching an episode this evening from season 4 where his Jeep literally shook itself apart. It's clearly one of the tropes of the show, but I'm wondering if the creators have ever explained why.
This was addressed in a Reddit AMA with actor Colin Ferguson who portrays Sheriff Carter. Evidently the running joke was a result of (positive) fan-reaction to seeing Carter looking pained at the loss of yet another jeep.
Q: Is there a reason the jeep always gets crushed?
CF: Not really, except Jaime [Ray Newman] figured out people enjoy seeing me frustrated...just like in life.
So it's a way to bug me :)
I'd say it's a way to introduce a running gag that will not screw up the whole continuity (see South Park's Kenny dieing over and over again in early episodes), while still taking some "key item" off the protagonists and being interesting (and funny, by adding new situations; e.g. Sarah driving him around).
Look around, there aren't that many other possibilities/possessions they could somehow take away in a more or less weird way, without introducing further issues:
They could blow up the sheriff's office or his house/Sarah (very costly or impossible to fix on a regular basis; wouldn't make sense).
They could kill characters (which would get old and isn't as funny as in a 2D colored paper animation series).
They could (and do) screw with Carter's daily live in some obscure ways (like having him to fill out weird documents or introducing some invention he's confronted with), but these aren't as special/impacting as a - yet again - destroyed car.